Here is the full list of all 16 Frozen Synapse achievements.
Complete the Single Player Campaign.
Get to Level 10.
Change the map generation settings.
Blow up the 4th wall in a level with a rocket launcher.
Win a game of Disputed.
Win a game of Charge.
Win a game of Hostage.
Win a game of Extermination.
Lose a unit to a rocket.
Lose your first multiplayer game.
Lose your first single-player mission.
Finish the tutorial.
Ignore an enemy.
Play an Instant Skirmish and win with only your machine gunner left alive.
Defeat 'Bin' in multiplayer.
Get to level 100.